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Math Help - calculus residue

  1. #1
    Junior Member
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    calculus residue

    hi everyone somebody knows to calculate the following residue of

    e^{-x z} \left(\text{Log}\left[\frac{1}{z}\right]\right) at z=0
    using Mathematica or maple gives
    0
    \text{Residue}\left[e^{-x z} \left(\text{Log}\left[\frac{1}{z}\right]\right),\{z,0\}\right] ==0 and using the definition of residue
    \text{Limit}\left[z \left(e^{-x z} \left(\text{Log}\left[\frac{1}{z}\right]\right)\right),z\to 0\right] gives 0 but i think it result is wrong.
    thanks any help
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  2. #2
    MHF Contributor chisigma's Avatar
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    Re: calculus residue

    Quote Originally Posted by capea View Post
    hi everyone somebody knows to calculate the following residue of

    e^{-x z} \left(\text{Log}\left[\frac{1}{z}\right]\right) at z=0
    using Mathematica or maple gives
    0
    \text{Residue}\left[e^{-x z} \left(\text{Log}\left[\frac{1}{z}\right]\right),\{z,0\}\right] ==0 and using the definition of residue
    \text{Limit}\left[z \left(e^{-x z} \left(\text{Log}\left[\frac{1}{z}\right]\right)\right),z\to 0\right] gives 0 but i think it result is wrong.
    thanks any help
    The Laurent expansion of the function \ln \frac{1}{z} = - \ln z around z=0 doesn't exist , and the same is for its residue in z=0... the question has been discussed in...

    http://www.mathhelpforum.com/math-he...st-167358.html

    Kind regards

    \chi \sigma
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